TSTP Solution File: SYN345+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN345+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 23:54:53 EDT 2022
% Result : Theorem 34.42s 22.43s
% Output : Proof 34.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYN345+1 : TPTP v8.1.0. Released v2.0.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Sep 5 02:58:40 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 34.42/22.43 % SZS status Theorem
% 34.42/22.43 % SZS output start Proof
% 34.42/22.43 tff(big_f_type, type, (
% 34.42/22.43 big_f: ( $i * $i * $i ) > $o)).
% 34.42/22.43 tff(tptp_fun_Z_2_type, type, (
% 34.42/22.43 tptp_fun_Z_2: ( $i * $i ) > $i)).
% 34.42/22.43 tff(tptp_fun_X2_0_type, type, (
% 34.42/22.43 tptp_fun_X2_0: $i)).
% 34.42/22.43 tff(elem_3_type, type, (
% 34.42/22.43 elem_3: $i)).
% 34.42/22.43 tff(tptp_fun_X1_1_type, type, (
% 34.42/22.43 tptp_fun_X1_1: $i)).
% 34.42/22.43 tff(1,plain,
% 34.42/22.43 (^[Y1: $i, Y2: $i] : refl((~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))))) <=> (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))))))),
% 34.42/22.43 inference(bind,[status(th)],[])).
% 34.42/22.43 tff(2,plain,
% 34.42/22.43 (![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))))) <=> ![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))),
% 34.42/22.43 inference(quant_intro,[status(thm)],[1])).
% 34.42/22.43 tff(3,plain,
% 34.42/22.43 (^[Y1: $i, Y2: $i] : rewrite((~((big_f(X2!0, X2!0, Y1) & (big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))) | (~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))))) <=> (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))))))),
% 34.42/22.43 inference(bind,[status(th)],[])).
% 34.42/22.43 tff(4,plain,
% 34.42/22.43 (![Y1: $i, Y2: $i] : (~((big_f(X2!0, X2!0, Y1) & (big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))) | (~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))))) <=> ![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))),
% 34.42/22.43 inference(quant_intro,[status(thm)],[3])).
% 34.42/22.43 tff(5,plain,
% 34.42/22.43 ((~![X1: $i, X2: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : ((big_f(X2, X2, Y1) & (big_f(X1, X1, X2) <=> big_f(X1, X2, X2))) | (~big_f(Y1, Y2, Z)) | (~(big_f(X1, X1, X2) | (~big_f(X1, X2, X2)) | (~((~big_f(X2, Y1, Y2)) | big_f(Y1, Z, Z))))) | (~(big_f(X1, X2, X2) | (~big_f(X1, X1, X2)) | (~((~big_f(X1, X2, Y1)) | big_f(Y2, Y1, Z))))))) <=> (~![X1: $i, X2: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : ((big_f(X2, X2, Y1) & (big_f(X1, X1, X2) <=> big_f(X1, X2, X2))) | (~big_f(Y1, Y2, Z)) | (~(big_f(X1, X1, X2) | (~big_f(X1, X2, X2)) | (~((~big_f(X2, Y1, Y2)) | big_f(Y1, Z, Z))))) | (~(big_f(X1, X2, X2) | (~big_f(X1, X1, X2)) | (~((~big_f(X1, X2, Y1)) | big_f(Y2, Y1, Z)))))))),
% 34.42/22.43 inference(rewrite,[status(thm)],[])).
% 34.42/22.43 tff(6,plain,
% 34.42/22.43 ((~![X1: $i, X2: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : (((big_f(X1, X2, Y1) => big_f(Y2, Y1, Z)) => (big_f(X1, X1, X2) => big_f(X1, X2, X2))) => (((big_f(X2, Y1, Y2) => big_f(Y1, Z, Z)) => (big_f(X1, X2, X2) => big_f(X1, X1, X2))) => (big_f(Y1, Y2, Z) => (big_f(X2, X2, Y1) & (big_f(X1, X1, X2) <=> big_f(X1, X2, X2))))))) <=> (~![X1: $i, X2: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : ((big_f(X2, X2, Y1) & (big_f(X1, X1, X2) <=> big_f(X1, X2, X2))) | (~big_f(Y1, Y2, Z)) | (~(big_f(X1, X1, X2) | (~big_f(X1, X2, X2)) | (~((~big_f(X2, Y1, Y2)) | big_f(Y1, Z, Z))))) | (~(big_f(X1, X2, X2) | (~big_f(X1, X1, X2)) | (~((~big_f(X1, X2, Y1)) | big_f(Y2, Y1, Z)))))))),
% 34.42/22.43 inference(rewrite,[status(thm)],[])).
% 34.42/22.43 tff(7,axiom,(~![X1: $i, X2: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : (((big_f(X1, X2, Y1) => big_f(Y2, Y1, Z)) => (big_f(X1, X1, X2) => big_f(X1, X2, X2))) => (((big_f(X2, Y1, Y2) => big_f(Y1, Z, Z)) => (big_f(X1, X2, X2) => big_f(X1, X1, X2))) => (big_f(Y1, Y2, Z) => (big_f(X2, X2, Y1) & (big_f(X1, X1, X2) <=> big_f(X1, X2, X2))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','church_46_16_4')).
% 34.42/22.43 tff(8,plain,
% 34.42/22.43 (~![X1: $i, X2: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : ((big_f(X2, X2, Y1) & (big_f(X1, X1, X2) <=> big_f(X1, X2, X2))) | (~big_f(Y1, Y2, Z)) | (~(big_f(X1, X1, X2) | (~big_f(X1, X2, X2)) | (~((~big_f(X2, Y1, Y2)) | big_f(Y1, Z, Z))))) | (~(big_f(X1, X2, X2) | (~big_f(X1, X1, X2)) | (~((~big_f(X1, X2, Y1)) | big_f(Y2, Y1, Z))))))),
% 34.42/22.43 inference(modus_ponens,[status(thm)],[7, 6])).
% 34.42/22.43 tff(9,plain,
% 34.42/22.43 (~![X1: $i, X2: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : ((big_f(X2, X2, Y1) & (big_f(X1, X1, X2) <=> big_f(X1, X2, X2))) | (~big_f(Y1, Y2, Z)) | (~(big_f(X1, X1, X2) | (~big_f(X1, X2, X2)) | (~((~big_f(X2, Y1, Y2)) | big_f(Y1, Z, Z))))) | (~(big_f(X1, X2, X2) | (~big_f(X1, X1, X2)) | (~((~big_f(X1, X2, Y1)) | big_f(Y2, Y1, Z))))))),
% 34.42/22.43 inference(modus_ponens,[status(thm)],[8, 5])).
% 34.42/22.43 tff(10,plain,
% 34.42/22.43 (~![X1: $i, X2: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : ((big_f(X2, X2, Y1) & (big_f(X1, X1, X2) <=> big_f(X1, X2, X2))) | (~big_f(Y1, Y2, Z)) | (~(big_f(X1, X1, X2) | (~big_f(X1, X2, X2)) | (~((~big_f(X2, Y1, Y2)) | big_f(Y1, Z, Z))))) | (~(big_f(X1, X2, X2) | (~big_f(X1, X1, X2)) | (~((~big_f(X1, X2, Y1)) | big_f(Y2, Y1, Z))))))),
% 34.42/22.43 inference(modus_ponens,[status(thm)],[9, 5])).
% 34.42/22.43 tff(11,plain,
% 34.42/22.43 (~![X1: $i, X2: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : ((big_f(X2, X2, Y1) & (big_f(X1, X1, X2) <=> big_f(X1, X2, X2))) | (~big_f(Y1, Y2, Z)) | (~(big_f(X1, X1, X2) | (~big_f(X1, X2, X2)) | (~((~big_f(X2, Y1, Y2)) | big_f(Y1, Z, Z))))) | (~(big_f(X1, X2, X2) | (~big_f(X1, X1, X2)) | (~((~big_f(X1, X2, Y1)) | big_f(Y2, Y1, Z))))))),
% 34.42/22.43 inference(modus_ponens,[status(thm)],[10, 5])).
% 34.42/22.43 tff(12,plain,
% 34.42/22.43 (~![X1: $i, X2: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : ((big_f(X2, X2, Y1) & (big_f(X1, X1, X2) <=> big_f(X1, X2, X2))) | (~big_f(Y1, Y2, Z)) | (~(big_f(X1, X1, X2) | (~big_f(X1, X2, X2)) | (~((~big_f(X2, Y1, Y2)) | big_f(Y1, Z, Z))))) | (~(big_f(X1, X2, X2) | (~big_f(X1, X1, X2)) | (~((~big_f(X1, X2, Y1)) | big_f(Y2, Y1, Z))))))),
% 34.42/22.43 inference(modus_ponens,[status(thm)],[11, 5])).
% 34.42/22.43 tff(13,plain,
% 34.42/22.43 (~![X1: $i, X2: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : ((big_f(X2, X2, Y1) & (big_f(X1, X1, X2) <=> big_f(X1, X2, X2))) | (~big_f(Y1, Y2, Z)) | (~(big_f(X1, X1, X2) | (~big_f(X1, X2, X2)) | (~((~big_f(X2, Y1, Y2)) | big_f(Y1, Z, Z))))) | (~(big_f(X1, X2, X2) | (~big_f(X1, X1, X2)) | (~((~big_f(X1, X2, Y1)) | big_f(Y2, Y1, Z))))))),
% 34.42/22.44 inference(modus_ponens,[status(thm)],[12, 5])).
% 34.42/22.44 tff(14,plain,
% 34.42/22.44 (~![X1: $i, X2: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : ((big_f(X2, X2, Y1) & (big_f(X1, X1, X2) <=> big_f(X1, X2, X2))) | (~big_f(Y1, Y2, Z)) | (~(big_f(X1, X1, X2) | (~big_f(X1, X2, X2)) | (~((~big_f(X2, Y1, Y2)) | big_f(Y1, Z, Z))))) | (~(big_f(X1, X2, X2) | (~big_f(X1, X1, X2)) | (~((~big_f(X1, X2, Y1)) | big_f(Y2, Y1, Z))))))),
% 34.42/22.44 inference(modus_ponens,[status(thm)],[13, 5])).
% 34.42/22.44 tff(15,plain,(
% 34.42/22.44 $oeq((~?[Y1: $i, Y2: $i] : ![Z: $i] : ((big_f(X2!0, X2!0, Y1) & (big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))) | (~big_f(Y1, Y2, Z)) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, Z, Z))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, Z))))))), ![Y1: $i, Y2: $i] : (~((big_f(X2!0, X2!0, Y1) & (big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))) | (~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))))))),
% 34.42/22.44 inference(transitivity,[status(sab)],[14])).
% 34.42/22.44 tff(16,plain,
% 34.42/22.44 (![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))),
% 34.42/22.44 inference(modus_ponens,[status(thm)],[15, 4])).
% 34.42/22.44 tff(17,plain,
% 34.42/22.44 (![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))),
% 34.42/22.44 inference(modus_ponens,[status(thm)],[16, 2])).
% 34.42/22.44 tff(18,plain,
% 34.42/22.44 (((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))) | (~((~((~big_f(X2!0, X2!0, X2!0)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))))) | big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))))) | (~big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))))))))) <=> ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))) | (~((~((~big_f(X2!0, X2!0, X2!0)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))))) | big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))))) | (~big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))))))))),
% 34.42/22.44 inference(rewrite,[status(thm)],[])).
% 34.42/22.44 tff(19,plain,
% 34.42/22.44 ((~((~big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))))) | big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))))) | (~((~big_f(X2!0, X2!0, X2!0)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))))) <=> (~((~((~big_f(X2!0, X2!0, X2!0)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))))) | big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))))) | (~big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))))))))),
% 34.42/22.44 inference(rewrite,[status(thm)],[])).
% 34.42/22.44 tff(20,plain,
% 34.42/22.44 (((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))) | (~((~big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))))) | big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))))) | (~((~big_f(X2!0, X2!0, X2!0)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))) <=> ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))) | (~((~((~big_f(X2!0, X2!0, X2!0)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))))) | big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))))) | (~big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))))))))),
% 34.42/22.44 inference(monotonicity,[status(thm)],[19])).
% 34.42/22.44 tff(21,plain,
% 34.42/22.44 (((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))) | (~((~big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))))) | big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))))) | (~((~big_f(X2!0, X2!0, X2!0)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))) <=> ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))) | (~((~((~big_f(X2!0, X2!0, X2!0)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))))) | big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))))) | (~big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))))))))),
% 34.42/22.44 inference(transitivity,[status(thm)],[20, 18])).
% 34.42/22.44 tff(22,plain,
% 34.42/22.44 ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))) | (~((~big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))))) | big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))))) | (~((~big_f(X2!0, X2!0, X2!0)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))),
% 34.42/22.44 inference(quant_inst,[status(thm)],[])).
% 34.42/22.44 tff(23,plain,
% 34.42/22.44 ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))) | (~((~((~big_f(X2!0, X2!0, X2!0)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))))) | big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))))) | (~big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))))))))),
% 34.42/22.44 inference(modus_ponens,[status(thm)],[22, 21])).
% 34.42/22.44 tff(24,plain,
% 34.42/22.44 (~((~((~big_f(X2!0, X2!0, X2!0)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))))) | big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))))) | (~big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))))))),
% 34.42/22.45 inference(unit_resolution,[status(thm)],[23, 17])).
% 34.42/22.45 tff(25,plain,
% 34.42/22.45 (((~((~big_f(X2!0, X2!0, X2!0)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))))) | big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))))) | (~big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))))))) | (big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))))) | big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))))),
% 34.53/22.45 inference(tautology,[status(thm)],[])).
% 34.53/22.45 tff(26,plain,
% 34.53/22.45 (big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))))) | big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))))),
% 34.53/22.45 inference(unit_resolution,[status(thm)],[25, 24])).
% 34.53/22.45 tff(27,assumption,((~((~big_f(X2!0, X2!0, X2!0)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))) | (~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, X2!0)) | big_f(X2!0, tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(X2!0, X2!0)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))))))), introduced(assumption)).
% 34.53/22.45 tff(28,plain,
% 34.53/22.45 (((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))) | (~((~((~big_f(X2!0, X2!0, X2!0)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))) | (~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, X2!0)) | big_f(X2!0, tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(X2!0, X2!0)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))))))))) <=> ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))) | (~((~((~big_f(X2!0, X2!0, X2!0)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))) | (~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, X2!0)) | big_f(X2!0, tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(X2!0, X2!0)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0)))))))))),
% 34.53/22.45 inference(rewrite,[status(thm)],[])).
% 34.53/22.45 tff(29,plain,
% 34.53/22.45 ((~((~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, X2!0)) | big_f(X2!0, tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(X2!0, X2!0)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0)))))) | (~((~big_f(X2!0, X2!0, X2!0)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))))) <=> (~((~((~big_f(X2!0, X2!0, X2!0)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))) | (~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, X2!0)) | big_f(X2!0, tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(X2!0, X2!0)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))))))))),
% 34.53/22.45 inference(rewrite,[status(thm)],[])).
% 34.53/22.45 tff(30,plain,
% 34.53/22.45 (((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, X2!0)) | big_f(X2!0, tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(X2!0, X2!0)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0)))))) | (~((~big_f(X2!0, X2!0, X2!0)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))) <=> ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))) | (~((~((~big_f(X2!0, X2!0, X2!0)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))) | (~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, X2!0)) | big_f(X2!0, tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(X2!0, X2!0)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0)))))))))),
% 34.53/22.45 inference(monotonicity,[status(thm)],[29])).
% 34.53/22.45 tff(31,plain,
% 34.53/22.45 (((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, X2!0)) | big_f(X2!0, tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(X2!0, X2!0)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0)))))) | (~((~big_f(X2!0, X2!0, X2!0)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))) <=> ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))) | (~((~((~big_f(X2!0, X2!0, X2!0)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))) | (~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, X2!0)) | big_f(X2!0, tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(X2!0, X2!0)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0)))))))))),
% 34.53/22.45 inference(transitivity,[status(thm)],[30, 28])).
% 34.53/22.45 tff(32,plain,
% 34.53/22.45 ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, X2!0)) | big_f(X2!0, tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(X2!0, X2!0)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0)))))) | (~((~big_f(X2!0, X2!0, X2!0)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))),
% 34.53/22.45 inference(quant_inst,[status(thm)],[])).
% 34.53/22.45 tff(33,plain,
% 34.53/22.45 ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))) | (~((~((~big_f(X2!0, X2!0, X2!0)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))) | (~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, X2!0)) | big_f(X2!0, tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(X2!0, X2!0)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))))))))),
% 34.53/22.45 inference(modus_ponens,[status(thm)],[32, 31])).
% 34.53/22.45 tff(34,plain,
% 34.53/22.45 ($false),
% 34.53/22.45 inference(unit_resolution,[status(thm)],[33, 17, 27])).
% 34.53/22.45 tff(35,plain,(~((~((~big_f(X2!0, X2!0, X2!0)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))) | (~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, X2!0)) | big_f(X2!0, tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(X2!0, X2!0)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0)))))))), inference(lemma,lemma(discharge,[]))).
% 34.53/22.45 tff(36,plain,
% 34.53/22.45 (((~((~big_f(X2!0, X2!0, X2!0)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))) | (~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, X2!0)) | big_f(X2!0, tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(X2!0, X2!0)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))))))) | big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))),
% 34.53/22.45 inference(tautology,[status(thm)],[])).
% 34.53/22.45 tff(37,plain,
% 34.53/22.45 (big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))),
% 34.53/22.45 inference(unit_resolution,[status(thm)],[36, 35])).
% 34.53/22.45 tff(38,assumption,((~big_f(tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0))) | big_f(tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0))))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0))))))) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))), introduced(assumption)).
% 34.53/22.45 tff(39,plain,
% 34.53/22.45 ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))) | (~((~big_f(tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0))) | big_f(tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0))))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0))))))) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))),
% 34.53/22.45 inference(quant_inst,[status(thm)],[])).
% 34.53/22.45 tff(40,plain,
% 34.53/22.45 ($false),
% 34.53/22.45 inference(unit_resolution,[status(thm)],[39, 17, 38])).
% 34.53/22.45 tff(41,plain,(~((~big_f(tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0))) | big_f(tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0))))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0))))))) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))))), inference(lemma,lemma(discharge,[]))).
% 34.53/22.45 tff(42,plain,
% 34.53/22.45 (((~big_f(tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0))) | big_f(tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0))))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0))))))) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))) | ((~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))),
% 34.53/22.45 inference(tautology,[status(thm)],[])).
% 34.53/22.45 tff(43,plain,
% 34.53/22.45 ((~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))),
% 34.53/22.45 inference(unit_resolution,[status(thm)],[42, 41])).
% 34.53/22.45 tff(44,plain,
% 34.53/22.45 ((~((~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))) | (~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))),
% 34.53/22.45 inference(tautology,[status(thm)],[])).
% 34.53/22.45 tff(45,plain,
% 34.53/22.45 ((~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))),
% 34.53/22.45 inference(unit_resolution,[status(thm)],[44, 43])).
% 34.53/22.46 tff(46,plain,
% 34.53/22.46 ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)),
% 34.53/22.46 inference(unit_resolution,[status(thm)],[45, 37])).
% 34.53/22.46 tff(47,assumption,(big_f(X1!1, X1!1, X2!0)), introduced(assumption)).
% 34.53/22.46 tff(48,plain,
% 34.53/22.46 (((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))) | (~((~big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, elem!3)) | big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3)))))) | (~((~big_f(X2!0, X2!0, elem!3)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, elem!3, elem!3)) | big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))))))))) <=> ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))) | (~((~big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, elem!3)) | big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3)))))) | (~((~big_f(X2!0, X2!0, elem!3)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, elem!3, elem!3)) | big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))))))))),
% 34.53/22.46 inference(rewrite,[status(thm)],[])).
% 34.53/22.46 tff(49,plain,
% 34.53/22.46 ((~((~big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, elem!3, elem!3)) | big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, elem!3)) | big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3)))))) | (~((~big_f(X2!0, X2!0, elem!3)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))))) <=> (~((~big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, elem!3)) | big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3)))))) | (~((~big_f(X2!0, X2!0, elem!3)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, elem!3, elem!3)) | big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))))))))),
% 34.53/22.46 inference(rewrite,[status(thm)],[])).
% 34.53/22.46 tff(50,plain,
% 34.53/22.46 (((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))) | (~((~big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, elem!3, elem!3)) | big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, elem!3)) | big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3)))))) | (~((~big_f(X2!0, X2!0, elem!3)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))) <=> ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))) | (~((~big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, elem!3)) | big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3)))))) | (~((~big_f(X2!0, X2!0, elem!3)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, elem!3, elem!3)) | big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))))))))),
% 34.53/22.46 inference(monotonicity,[status(thm)],[49])).
% 34.53/22.46 tff(51,plain,
% 34.53/22.46 (((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))) | (~((~big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, elem!3, elem!3)) | big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, elem!3)) | big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3)))))) | (~((~big_f(X2!0, X2!0, elem!3)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))) <=> ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))) | (~((~big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, elem!3)) | big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3)))))) | (~((~big_f(X2!0, X2!0, elem!3)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, elem!3, elem!3)) | big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))))))))),
% 34.53/22.46 inference(transitivity,[status(thm)],[50, 48])).
% 34.53/22.46 tff(52,plain,
% 34.53/22.46 ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))) | (~((~big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, elem!3, elem!3)) | big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, elem!3)) | big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3)))))) | (~((~big_f(X2!0, X2!0, elem!3)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))),
% 34.53/22.46 inference(quant_inst,[status(thm)],[])).
% 34.53/22.46 tff(53,plain,
% 34.53/22.46 ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))) | (~((~big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, elem!3)) | big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3)))))) | (~((~big_f(X2!0, X2!0, elem!3)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, elem!3, elem!3)) | big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))))))))),
% 34.53/22.46 inference(modus_ponens,[status(thm)],[52, 51])).
% 34.53/22.46 tff(54,plain,
% 34.53/22.46 (~((~big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, elem!3)) | big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3)))))) | (~((~big_f(X2!0, X2!0, elem!3)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, elem!3, elem!3)) | big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))))))),
% 34.53/22.46 inference(unit_resolution,[status(thm)],[53, 17])).
% 34.53/22.46 tff(55,plain,
% 34.53/22.46 (((~big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, elem!3)) | big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3)))))) | (~((~big_f(X2!0, X2!0, elem!3)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, elem!3, elem!3)) | big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))))))) | (big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, elem!3)) | big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3)))))),
% 34.53/22.46 inference(tautology,[status(thm)],[])).
% 34.53/22.46 tff(56,plain,
% 34.53/22.46 (big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, elem!3)) | big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3))))),
% 34.53/22.46 inference(unit_resolution,[status(thm)],[55, 54])).
% 34.53/22.46 tff(57,plain,
% 34.53/22.46 (((~big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, elem!3)) | big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3)))))) | (~((~big_f(X2!0, X2!0, elem!3)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, elem!3, elem!3)) | big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))))))) | big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3))),
% 34.53/22.46 inference(tautology,[status(thm)],[])).
% 34.53/22.46 tff(58,plain,
% 34.53/22.46 (big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3))),
% 34.53/22.46 inference(unit_resolution,[status(thm)],[57, 54])).
% 34.53/22.46 tff(59,plain,
% 34.53/22.46 (((~big_f(X1!1, X2!0, elem!3)) | big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3))) | (~big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3)))),
% 34.53/22.46 inference(tautology,[status(thm)],[])).
% 34.53/22.46 tff(60,plain,
% 34.53/22.46 ((~big_f(X1!1, X2!0, elem!3)) | big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3))),
% 34.53/22.46 inference(unit_resolution,[status(thm)],[59, 58])).
% 34.53/22.46 tff(61,plain,
% 34.53/22.46 ((~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, elem!3)) | big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3)))))) | big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, elem!3)) | big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3))))),
% 34.53/22.46 inference(tautology,[status(thm)],[])).
% 34.53/22.46 tff(62,plain,
% 34.53/22.46 (big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0))),
% 34.53/22.46 inference(unit_resolution,[status(thm)],[61, 60, 56])).
% 34.53/22.46 tff(63,plain,
% 34.53/22.46 (big_f(X1!1, X2!0, X2!0)),
% 34.53/22.46 inference(unit_resolution,[status(thm)],[62, 47])).
% 34.53/22.46 tff(64,plain,
% 34.53/22.46 ((~((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))) | (~big_f(X1!1, X1!1, X2!0)) | (~big_f(X1!1, X2!0, X2!0))),
% 34.53/22.46 inference(tautology,[status(thm)],[])).
% 34.53/22.46 tff(65,plain,
% 34.53/22.46 ($false),
% 34.53/22.46 inference(unit_resolution,[status(thm)],[64, 63, 47, 46])).
% 34.53/22.46 tff(66,plain,(~big_f(X1!1, X1!1, X2!0)), inference(lemma,lemma(discharge,[]))).
% 34.53/22.46 tff(67,plain,
% 34.53/22.46 ((~((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))) | big_f(X1!1, X1!1, X2!0) | big_f(X1!1, X2!0, X2!0)),
% 34.53/22.46 inference(tautology,[status(thm)],[])).
% 34.53/22.46 tff(68,plain,
% 34.53/22.46 (big_f(X1!1, X2!0, X2!0)),
% 34.53/22.46 inference(unit_resolution,[status(thm)],[67, 66, 46])).
% 34.53/22.46 tff(69,plain,
% 34.53/22.46 ((~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))))) | big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))))) | big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))))) | big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))))),
% 34.53/22.46 inference(tautology,[status(thm)],[])).
% 34.53/22.46 tff(70,plain,
% 34.53/22.46 ((~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))))) | big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))))) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))))) | big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))))),
% 34.53/22.46 inference(unit_resolution,[status(thm)],[69, 68, 66])).
% 34.53/22.46 tff(71,plain,
% 34.53/22.46 (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))))) | big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))),
% 34.53/22.46 inference(unit_resolution,[status(thm)],[70, 26])).
% 34.53/22.46 tff(72,plain,
% 34.53/22.46 (((~big_f(X2!0, X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))))) | big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | (~big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))),
% 34.53/22.46 inference(tautology,[status(thm)],[])).
% 34.53/22.46 tff(73,plain,
% 34.53/22.46 (~big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))),
% 34.53/22.46 inference(unit_resolution,[status(thm)],[72, 71])).
% 34.53/22.46 tff(74,plain,
% 34.53/22.46 (((~big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))) | big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))),
% 34.53/22.46 inference(tautology,[status(thm)],[])).
% 34.53/22.46 tff(75,plain,
% 34.53/22.46 ((~big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))),
% 34.53/22.47 inference(unit_resolution,[status(thm)],[74, 73])).
% 34.53/22.47 tff(76,plain,
% 34.53/22.47 ((~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))))))) | big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))))),
% 34.53/22.47 inference(tautology,[status(thm)],[])).
% 34.53/22.47 tff(77,plain,
% 34.53/22.47 (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))))))),
% 34.53/22.47 inference(unit_resolution,[status(thm)],[76, 68, 66, 75])).
% 34.53/22.47 tff(78,plain,
% 34.53/22.47 (((~big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))))))) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))))))) | (big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))))))),
% 34.53/22.47 inference(tautology,[status(thm)],[])).
% 34.53/22.47 tff(79,plain,
% 34.53/22.47 ((~big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))))))) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))))))),
% 34.53/22.47 inference(unit_resolution,[status(thm)],[78, 77])).
% 34.53/22.47 tff(80,plain,
% 34.53/22.47 (((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))) | (~((~big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))))))) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))))))))) <=> ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))) | (~((~big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))))))) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))))))))))),
% 34.55/22.47 inference(rewrite,[status(thm)],[])).
% 34.55/22.47 tff(81,plain,
% 34.55/22.47 ((~((~big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))))))) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))))) <=> (~((~big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))))))) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))))))))),
% 34.55/22.48 inference(rewrite,[status(thm)],[])).
% 34.55/22.48 tff(82,plain,
% 34.55/22.48 (((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))) | (~((~big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))))))) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))) <=> ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))) | (~((~big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))))))) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))))))))))),
% 34.55/22.48 inference(monotonicity,[status(thm)],[81])).
% 34.55/22.48 tff(83,plain,
% 34.55/22.48 (((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))) | (~((~big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))))))) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))) <=> ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))) | (~((~big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))))))) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))))))))))),
% 34.55/22.48 inference(transitivity,[status(thm)],[82, 80])).
% 34.55/22.48 tff(84,plain,
% 34.55/22.48 ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))) | (~((~big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))))))) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))),
% 34.55/22.49 inference(quant_inst,[status(thm)],[])).
% 34.55/22.49 tff(85,plain,
% 34.55/22.49 ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0))))))) | (~((~big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))))))) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | ((~big_f(X1!1, X1!1, X2!0)) <=> big_f(X1!1, X2!0, X2!0)))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)), tptp_fun_Z_2(X2!0, tptp_fun_Z_2(tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(X1!1, tptp_fun_Z_2(elem!3, elem!3))))), X2!0)))))))))),
% 34.55/22.49 inference(modus_ponens,[status(thm)],[84, 83])).
% 34.55/22.49 tff(86,plain,
% 34.55/22.49 ($false),
% 34.55/22.49 inference(unit_resolution,[status(thm)],[85, 17, 79])).
% 34.55/22.49 % SZS output end Proof
%------------------------------------------------------------------------------